What are gravitons made of? And how do they cause gravity? What are gravitons made of and how do they cause gravity? Why do bodies with more mass attract more gravitons and hence have a greater gravitational pull? I heard that nobody quite exactly knows this (officially), but somebody might. Does anybody know?
 A: 
What are gravitons made of

They are made of nothing as they are elementary particles.  That is, there are no compnent of a graviton.  We have not detected gravitons and do not know for sure they exist.  They're kind of "pencilled in" as something we think we need.

and how do they cause gravity ?

Good question.  There is no complete theory for this (or as we say technically "we don't know").
They are expected to act in a similar role to photons in the Quantum Theory of Electrodynamics (QED), but whereas we have a well refined theory of QED that has been very well tested, we have no well defined theory of gravity using gravitons and no tests at all.  Quantum gravity is proving a lot more difficult to develop than the already complex QED and similar field theories.

Why do bodies with more mass attract more gravitons

Do they ?  We have no theory for this.

and hence have a greater gravitational pull?


I heard that nobody quite exactly knows this (officially), but somebody might. Does anybody know?

There are multiple theories exploring what is loosely termed quantum gravity, but none are completely worked out, some have problem and some cannot be tested hence we have no way to answer this beyond "don't know (officially) yet".
Lots of people think they know unofficially ("have a theory they favor") but in science it the official part that you need. One of the comments mentioned supersymmetric strings, but this is by no means the way everyone thinks.  It's one of several approaches being explored at this time.
A: Gravitons, if they exist, are excitations of the gravitational field, much as photons are excitations of the electromagnetic field. Real gravitons would be observed as gravitational waves (just as real photons are seen as electromagnetic waves, e.g. light).
To say that gravitons "cause" gravity would be a gross oversimplification; technically what would be happening is that gravity would be modeled in the field theory as an exchange of virtual gravitons. The field is the more fundamental object in quantum field theory. You could loosely think of it as a massive body having a stronger gravitational field nearby, which in turn means more virtual gravitons popping in and out of existence near it; but this would be very loose indeed.
In any case this is all speculation, since the quantum theory of gravity is still an active area of research, and nobody knows whether gravitons actually exist.
